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The leader–following consensus of linear heterogeneous multiagent systems is investigated in this paper. To comply with the most practical scenario, the communicating topologies among agents are assumed to switch stochastically and driven by a continuous‐time discrete‐state Markov process, whose state space corresponds to all the possible topologies. A novel distributed adaptive compensator is designed for the followers to reconstruct the exogenous signals without knowing the Laplacian matrix who is regarded as a global information, and sufficient conditions are given to ensure the compensator converges to the dynamic of the leader asymptotically in the mean square sense. Then, based on the compensator, we solved the consensus problem both by distributed state and measurement output feedback control schemes under output regulation framework, which allow followers to have nonidentical state dimensions. Finally, the theoretical results are demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

The robust leader‐following consensus of heterogeneous multiagent systems under switching communication topologies is investigated in this paper. Especially, the input delay is considered in each follower. In order to access the information of leader through time‐varying communication, a type of distributed dynamic compensator is proposed for every follower firstly, which get rid of the dependence on the global spectrum information and is proved that it can be viewed as a asymptotic observer of the leader. Then combined with the internal model principle, two types of distributed control law are proposed based on the compensator. By applying the truncated predictor feedback scheme to synthesize the closed‐loop systems, it is proved that the consensus can be achieved by both of the control laws despite the existence of the input delay and the plant parameters perturbations. Finally, numerical simulations are illustrated to demonstrate the results. [ABSTRACT FROM AUTHOR]

This paper focuses on the robust mean-square consensus control problem for linear multiagent systems over randomly switching signed interaction topologies. The stochastic process is governed by a time-homogeneous Markov chain with partly unknown transition rates. Sufficient conditions for a consensus in the form of linear matrix inequalities are given via distributed adaptive control based on parameter-dependent Lyapunov functions. The adaptive control protocols require only the neighbor information of the agents, and the algorithm that designs the protocols reduces the influence of the communication topology on the consensus, which can prevent undesirable interaction impacts. Moreover, the disturbance rejection problem is addressed as an extension. Finally, two simulations are utilized to illustrate the effectiveness of the algorithms. [ABSTRACT FROM AUTHOR]

The consensus problem is considered for multi-agent systems with disturbances. Three fixed-time prescribed performance methods are proposed to satisfy the transient performance and steady-state performance of multi-agent systems consensus. If the multi-agent systems are affected by matched disturbances, the consensus tracking errors constraints are guaranteed at first. Next, the consensus tracking errors constraints and their change rates constraints are further considered. Moreover, with the help of a fixed-time observer, the consensus tracking errors constraints result is expended to the case of multi-agent systems affected by mismatched disturbances. The proposed methods can provide the satisfactory system performances, including that consensus tracking errors always evolve within predefined bounds, converge to a small closed region containing zero in fixed time and then converge to zero asymptotically. Simulations are provided to verify the effectiveness of the proposed methods. • A problem of fixed-time multi-agent systems consensus is considered. • Both the transient and steady-state performances of multi-agent systems can be guaranteed. • The anti-disturbance controllers can deal with mismatched/matched disturbances. • Three different controllers are available for different cases and performance objectives. [ABSTRACT FROM AUTHOR]

In this paper, the problem of reachable set estimation of multi-agent systems (MASs) is investigated. For the ease of application, balanced communication topology with a directed spanning tree and non-zero initial condition are considered. Based on the Lyapunov method and orthogonal transformation technique, sufficient conditions are established in terms of linear matrix inequalities to guarantee that the reachable set of MASs is bounded by a compact ellipsoid. Moreover, by employing some useful skills from stochastic analysis, the result is then extended to the problem for MASs under Markovian switching topologies. The effectiveness of the obtained results is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

In the paper, the robust consensus control is investigated for a class of second-order multi-agent systems with time-varying interaction topology and disturbances. Firstly, due to the variation considered being bounded, the topology is modeled as time-varyingly uncertain topology with polytopic type. Then, regarding the uncertain parameters as independent variables and formulating the multi-agent system as a special polynomial system, the robust consensus problem is converted to the robust stability analysis of the error model via stability theory of control systems. Furthermore, the idea is generalized to study the disturbance attenuation problem. Sufficient conditions for the solutions to the robust consensus problems without and with disturbance attenuation are formulated in terms of homogeneous parameter-dependent linear matrix inequalities (HPD-LMIs) which can be solved via semidefinite programming relaxations based on the sum of squares technique. Finally, simulation results are provided to illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

This paper studies the robust consensus problem for a class of linear multi-agent systems (MASs) with polytopic uncertainties and external disturbances. The uncertainties appear in both the dynamics of each agent and the topology of the overall network. Based on Lyapunov stability theory, the robust consensus problem is converted to the robust H ∞ stabilization of the error system. With the aid of the homogeneous parameter-dependent (HPD) Lyapunov functions and sum of squares (SOS) technique, the robust consensus problem is further formulated as an SOS programming. Sufficient conditions to achieve robust consensus with disturbance rejection capability are presented in terms of SOS constraints. As an extension, the robust consensus problem for discrete-time MASs is studied in a similar way. Numerical examples are provided to illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

• A distributed adaptive control methodology is proposed to solve the mean-square consensus control problem. • Parameter-dependent Lyapunov functions and free-weighting matrix methods are introduced. • The controllers are independent of randomly switching topologies. • The disturbance rejection performance of MASs over switching topologies are also discussed. This paper considers the stochastic consensus problem of high-order linear discrete-time multiagent systems (MASs) with uncertain topologies and external disturbances. The randomly switching interaction signed topologies are governed by a time-homogenous Markov chain with incomplete knowledge of the transition probabilities. Based on Lyapunov function theory and adaptive control strategies, we employ a homogeneous parameter-dependent Lyapunov function to propose sufficient conditions under a set of linear matrix inequality (LMI) constraints. A free-weighting matrix method is introduced to give the proposed LMIs extra freedom to search feasible solutions. Furthermore, the adaptive controllers applied in this paper are independent of topologies and fully distributed; i.e., the system achieves robust consensus without continuously updating the controller and dealing with global data. Additionally, we extend the theoretical framework to analyze the disturbance rejection performance of MASs under the stochastic process. Two numerical examples are provided to show the effectiveness of the algorithms. [ABSTRACT FROM AUTHOR]